CADILLAC CTS BATTERY PROBLEM

Smoking from where? Under the hood? Tail pipe? If the smoke is coming from under the hood, oil probably ran down when the valve cover was off and got onto hot exhaust parts. That smoke will gradually go away. Normally mechanics will wash the area of oil residue when they're done, but oil and the cleaning chemicals can pool in hidden places, then get hot later when you drive the car, and start to boil off.

Forgot to mention that GM has a design problem with their generators that results in a lot of failures. It is common to go through four to six of them in the life of the car. To reduce the number of repeat failures, replace the battery at the same time unless it is less than about two years old. The battery absorbs and dampens the huge voltage spikes these generators produce, and it loses its ability to do that when they get older.